Structure properties of W matrices

AbstractWe continue an investigation of the class W of real square matrices. A matrix belongs to W if and only if certain pairs of its complementary cones intersect in the zero vector only. We show that a W matrix with no zero diagonal entries is a P0 matrix (each principal minor is nonnegative), and a W matrix with no nonzero diagonal entries is a nonnegative matrix which either is monomial or has a zero column. Lastly, we show how these two results impose certain necessary conditions on the structure of a W matrix